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An atomic orbital is a mathematical function that describes the wave-like behavior of an electron in an atom. This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom's nucleus. The term "orbital" has become known as either the "mathematical function" or the "region" generated with the function.[1] Specifically, atomic orbitals are the possible quantum states of an individual electron in the electron cloud around a single atom, as described by the function.

The idea that electrons moved in an orbit-like way inside an atom, was first suggested in 1904. From about 1913 to 1926 the electrons were thought to orbit the atomic nucleus much like the planets around the Sun. Explaining the behavior of the electron "orbits" was one of the driving forces behind the development of quantum mechanics. In quantum mechanics, atomic orbitals are described as wave functions over space, indexed by the n, l, and m quantum numbers of the orbital or by the names as used in electron configurations, as shown on the right. As electrons cannot be described as solid particles (like a planet), a more accurate analogy to the electron would be that of a large and often oddly-shaped atmosphere, the electron, distributed around a relatively tiny planet, which is the atomic nucleus. Because of the difference from classical mechanical orbits, the term "orbit" for electrons in atoms, has been replaced with the term orbital.

The orbital names (s, p, d, f, g, h,...) are derived from the characteristics of their spectroscopic lines sharp, principal, diffuse, and fundamental, the rest being named in alphabetical order.

Orbitals are given names in the form

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